Your code can be simplified to

farey := proc(N::posint) local a,b; sort([op({seq(seq(a/b,a=0..b),b=1..N)})]) end proc;

You were doing O(N^4) work when O(N^2) is sufficient.  Then with that you can do

L:= N-> nops(farey(N)):
p1 := plots[listplot]([seq([n,3*n^2/L(n)],n=1..50)]):
p2 := plot(Pi^2,1..50):
plots[display](p1,p2);

which is likely what you want.

If you posted Maple input for your question, you might get more takers.

Robert is correct that rsolve won't help you at all here.  But it looks like you are really studying time series -- have you looked into the Statistics package instead? 

Look at ?plot,coords and ?plots,contourplot.

Some operations cannot be interrupted -- although most can.  Unfortunately, Matrix operations are one of those non-interruptible operations.

On the other hand, that Matrix is tiny, the context menus should be really fast for that (or at least they were for Maple 6, 7, and 8).  Which version are you using?  It is possible that some serious inefficiency has been introduced in the context menu code.

Maple 10 had all sorts of problems with Vista, but 11 seems fine.  I am writing this on a Vista laptop (woe be me, I know), but Maple seems fine.  Although I admit I most use Classic...

Are you sure you are running the same version of the MapleNet server as is used for this site?  [And don't assume that this site uses the latest version...  Maplesoft is very conservative in its software upgrades of important systems.]

On expressions such as the one you gave, Maple's simplify should itself take care of trying radnormal.  It is surprising that it does not.  Have you filed a bug report?

you need to tell us a bit more about your problem.  Just posting the one (huge) command is unlikely to motivate people to look at it.  And when a problem is so big, then using a worksheet with the justification and the command together is often a good idea.

If you have the full MathType, I believe it understands MathML.  It used to be that Maple posted to the clipboard in multiple formats, including MathML -- at least Classic does/did.  Then you can just paste in the MathML.  If that doesn't work, then you can choose the 'convert to MathML' from the context menu, copy that, and paste it in.  Hopefully that will work.

C'est possible de faire fontionner un Maplet en utilisant MapleNet, mais je dois dire que je ne me souviens plus comment.  C'est dans la doc the MapleNet.  Sinon il faut ecrire a Maplesoft (support@maplesoft.com), ils devraient pouvoir vous indiquer quelle partie de la doc il faut lire.

What version of Maple are you using?  In my Maple 11, I do not see those errors.

Since you are doing kinematics, instead of using a moving frame [as you implicitly do in your formulation by putting some particles in a specifc location], use a fixed frame but do things in terms of the path of the atoms.  Your initial conditions will still be algebraic, as above.  But then your conditions will be in such a way as to give you a system of ODEs with conditions in exactly the way that the new numerical solvers can handle.

One way to do this is as a system of polynomial equations and inequalities.  It is best to deal with the square of the distance instead of the distance itself [since that removes an unecessary square-root]. 

When you have a specific distance, then you can do something like (a4-a3)^2 + (b4-b3)^2 + c4^2 = d23, and inequalities in the same way.  Unfortunately, "resolving" such a system requires a CAD algorithm which, even after all these years, Maple still does not have.  Its main competitors do.

My advice: learn how to do this by hand.  If you don't, you'll flunk your tests.

But if you want to check your answers with maple, then the command diff is what you are looking for.